Failure of the trilinear operator space Grothendieck theorem

Abstract

We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on ${\ell }_{\infty }$, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded, answering a question of Pisier. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.

Reformatted for Discrete Analysis

References in corpus (3)

• Unbounded violation of tripartite Bell inequalities
• Operator algebraic approach to inverse and stability theorems for amenable groups
• Quantum Query Algorithms are Completely Bounded Forms

Cited by in corpus (1)

• Grothendieck inequalities characterize converses to the polynomial method